Sliding Mode Control For Discrete-time Systems Based On Predictive Control Strategy

Half century has passed since the appearance of sliding mode control (SMC), however, most of the research results are about continuous-time systems. With the development of computers technology and the widespread of digital controllers/manipulators, the investigation of SMC for discrete-time systems becomes intensive among researchers and engineers. Considering the shortcomings of the conventional SMC, such as great control signal is required to drive system states arrive sliding mode surface, the robustness depends on the upper bound of uncertainties and so on, predictive control strategy is introduced into the design of SMC in this thesis. For general linear systems and some classes of nonlinear systems, focusing on the stabilization problem and tracking problem, using the principles of General Predictive Control (GPC) and Model Algorithmic Control (MAC), several sliding mode predictive models are constructed. By choosing different kinds of sliding mode reference trajectory, employing feedback correction and receding horizon optimization approaches, discrete-time sliding mode controllers which fit to corresponding systems, are obtained. Theoretical analysis and simulation results indicate the advantages of the presented predictive sliding mode control method over the conventional SMC methods. The height control of helicopter and the level control of tank experiments verify the practical efficiency of the proposed methods.The primary results of this thesis can be described as follows,1. For the systems described by Controlled Auto-Regressive Integrated Moving Average (CARIMA) model, the general predictive sliding mode control algorithm is proposed. The design of this algorithm is comprised of four stages: firstly, after giving the desired sliding surface, the sliding mode prediction model (SMPM) is created based on the adjoint matrix of the system, such that the future information of sliding mode can be used; secondly, in order to force the system states to sliding surface smoothly, a suitable sliding mode reference trajectory (SMRT) is designed; thirdly, by defining a performance index which is relatives to the output of SMPM, and then due to receding horizon optimization, the incremental general predictive sliding mode controller is obtained; fourthly, parameter identification is used to identify the parameters in CARIMA model. Because GPC can deal with control time-delay conveniently, our algorithm can be extended to control time-delay systems.2. For general discrete-time linear systems, the tracking problem for known motion is considered. In order to make systems have robustness to matched /unmatched uncertainties, and have optimal control signals, model predictive control (MPC) strategy is combined with SMC. Due to global sliding mode approach, a novel SMPM is constructed. Based on first-order process, SMRT is created, so to guarantee the desired reaching mode. Due to feedback correction and receding horizon optimization, the uncertainties can be compensated in time, no matter the uncertainties are satisfied matched condition or not. Quadratic form performance index which includes the control penalty term, can adjust the influence of sliding mode predictive error and control input in the index. Solving the index, the non-switching type discrete-time sliding mode controller is obtained, thus the chattering will not appear in the system. Rigor theoretic proof verifies the robust stability of the closed-loop systems.3. For a class of systems which can separate to linear component and nonlinear component, by linearizing the nonlinear feedback loop with respect to a known reference trajectory in prediction horizon , a linear time-vary (LTV) system model is gotten. After assigning a suitable sliding surface which can guarantee the stability of ideal sliding mode, according to the gotten LTV model, a time-vary SMPM is given. By feedback correction and receding horizon optimization, for the case of no constraint, the optimal control signal is obtained. In a numerical example, compared with conventional DSMC, the presented algorithm makes the closed-loop system possess stronger robustness and faster convergence, and no chattering. When the solution of the optimization problem exists, the proposed algorithm fits to systems with constraints. Because the nonlinear model is converted to time-vary linear model, the optimization problem is quadratic programming not nonlinear programming, the computational complexity is reduced.4. The SMC is constructed to deal with Brunowsky-like canonical form nonlinear systems. A sliding surface which possesses desired dynamic, is designed at first. By creating a time-vary SMPM, employing feedback correction to compensate the influence of uncertainties, and using receding horizon optimization, the optimal discrete-time sliding mode controller is obtained. Theoretical analysis shows the closed-loop systems is robust stable, the upper bounds of uncertainties are not required, and the quasi-sliding mode band is tiny when the sampling period is small or the uncertainties have slow change rates. Numerical results indicates the presented algorithm guarantees the closed-loop system has stronger robustness, faster convergence and lower peak value in control signal, compared with the conventional reaching law DSMC method.5. For a class of discrete-time coupled nonlinear uncertain systems, enlighten by recursive sliding mode approach, a special SMPM is presented. Considered model mismatching, the error between the output of SMPM and real switching function value is used to make feedback correction. Due to receding horizon optimization, non-switching type discrete-time sliding mode controller is obtained. Because of feedback correction and receding horizon optimization, the influence of uncertainties is compensated immediately, the closed-loop system possesses strong robustness to matched or unmatched uncertainties as a result. Theoretic analysis proofs that the closed-loop system is robust stable even though the upper bounds of uncertainties and external disturbances are unknown. The results of a numerical example and a two-link rotational inverted pendulum illustrate the efficiency of the presented algorithm.The conclusion and perspective are given at the end of the dissertation.